Outgoing Football Association chairman Greg Dyke has questioned why anybody would want to manage England - while claiming the players looked 'scared' during the defeat to Iceland on Monday night.
Roy Hodgson resigned in the immediate aftermath of the result in Nice, sparking another frenzy of speculation as to who should lead the nation when World Cup qualifying begins in September.
But Dyke - who leaves the FA next month after three years in charge - acknowledges the problems within the national set-up appear to run deeper than just the need for a new man in charge.
"The new man has got to be somebody who really knows English football," he told The Guardian. "But there are loads of them now, more of them than there are English.
"You need someone who knows about English football. But Martin Glenn [FA chief executive] made clear you go for the best person. The harder question is why anybody would want it."
It has been suggested there is a psychological problem within the minds of the England players, and Dyke believes this theory does carry some weight.
He said: "I met Glenn Hoddle on the plane on the way back, and he said they were scared to death.
"Once you go 2-1 down, the longer it went on, the more scared they were. They brought on Marcus Rashford, who's 18, he's got nothing to lose, he wasn't scared at all. He was on for five minutes, he went past him three times. Once he lost the ball but twice he went through.
"They were just scared. It's the same in all sport. Really talented sportsmen can just freeze. That's what happens. Why do we not do well in competitions, in a tournament, when we won every game in qualifying?
"We beat much better sides in the run-up to it than Iceland. Why, what's that about? We need to understand that. And in the end you have got to get into the fact we have got fewer and fewer English players to choose from."
Gareth Southgate led the U21s to victory at the Toulon Tournament last month and remains favourite for the post ahead of ex-England manager Glenn Hoddle, United States boss Jurgen Klinsmann and Sunderland's Sam Allardyce.
The latter would be former FA chairman David Bernstein's choice if they plumped for a home-grown boss, although, like Dyke he says there is problem with the mindset of the current crop.
"I'm not saying we should have an English manager," he told the Daily Telegraph. "But, of the English managers, I actually would go for Sam Allardyce.
"He's a very powerful character. I think he's got the personality, the strength, he's a good technical manager, he's very experienced and he's someone who perhaps could imbue confidence.
"Because, clearly among other things, there's a psychological problem with our players, where they seem to get to a stage with international football where they just can't cope, and that's manifest time and time again, year after year, in individual errors which you just wouldn't expect from players.
"You had Steven Gerrard's error at the World Cup last time which cost us, you've got goalkeeping errors. A general psychological malaise seems to overcome them. They seem to freeze."